Comment: Every few years the media runs stories about "the oldest domain
name on the Internet". It appears that this is in response to being
contacted by the owners of symbolics.com. They appears to promote
themselves to journalists and bloggers as the oldest domain name.

It seems to me the confusion is simply over what is the oldest commercial domain name. symbolics.com was, according to many reliable sources, the first .com domain name, not the first domain name registered. (As for the first domain name registered, I don't know that the one listed is correct. Perhaps it comes down to what is meant by "registered" since testing of DNS went on for over a year and a half before, for example, the name mentioned was registered.)

URLs were first used in early 1983 on Arpanet when the Domain Name System was first established by GADS taskforce. Commercial URLs was not issued by ICAAN until 1985, with Symbolic.com being the first commercially registered domain name.

It's also worth mentioning that even though the .com TLD was opened back then, commercial use was very restricted until 1991 when it was permitted on a limited basis and finally 1995 when commercial restrictions were removed. By that time, Symbolics (with an s by the way) had already gone belly up. They did manage to hold on to their domain name until 2009.